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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Branched extensions of curves in compact surfaces

Author: Cloyd L. Ezell
Journal: Trans. Amer. Math. Soc. 259 (1980), 533-546
MSC: Primary 57M12; Secondary 30C15
MathSciNet review: 567095
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Abstract: A polymersion is a map $ F:\,M\, \to \,N$ where M and N are compact surfaces, orientable or nonorientable, M a surface with boundary, where

(a) At each interior point of M, there is an integer $ n\, \geqslant \,1$ such that F is topologically equivalent to the complex map $ {z^n}$ in a neighborhood about the point.

(b) At each point x in the boundary of M, $ \delta M$, there is a neighborhood U containing x such that U is homeomorphic to F(U).

A normal polymersion is one where $ F(\delta M)$ is a normal set of curves in N. We are concerned with establishing a combinatorial representation for normal polymersions which map to arbitrary compact surfaces.

References [Enhancements On Off] (What's this?)

  • [1] D. R. J. Chillingworth, Winding numbers on surfaces. I, Math. Ann. 196 (1972), 218-249. MR 0300304 (45:9350)
  • [2] G. K. Francis, Assembling compact Riemann surfaces with given boundary curves and branch points on the sphere, Illinois J. Math. 20 (1976), 198-217. MR 0402776 (53:6590)
  • [3] C. L. Ezell and M. L. Marx, Branched extensions of curves in orientable surfaces, Trans. Amer. Math. Soc. 259 (1980), 515-532. MR 567094 (81i:57004a)
  • [4] M. L. Marx and R. Verhey, Interior and polynomial extensions of immersed circles, Proc. Amer. Math. Soc. 24 (1970), 41-49. MR 0252660 (40:5879)
  • [5] J. Milnor, Topology from the differentiable viewpoint, Univ. Press of Virginia, Charlottesville, Va., 1965.s MR 0226651 (37:2239)

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Keywords: Polymersion, normal curve, assemblage, extension of a normal curve
Article copyright: © Copyright 1980 American Mathematical Society

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